Answer:
The answer to your question is
x = -2 and y = 10 or x = 10 and y = -2
Step-by-step explanation:
x + y = 8 (1) from (1) x = 8 - y
xy = - 20 (2)
Solve them by substitution
(8 - y) y = - 20
8y - y² = -20
y² - 8y - 20 = 0
( y - 10) (y + 2) = 0
y - 10 = 0 and y + 2 = 0
<u> y1 = 10 </u> <u>y2 = -2</u>
x1 = 8 - 10 x2 = 8 - -2
<u>x1 = -2</u> <u> x2 = 10</u>
Well, is just their difference, let's first convert the mixed fraction to "improper" and then subtract.
Well .5 for coin toss and with 52 cards in deck and clubs and spades makes it 26 so its 1/26 then those are your probabilities.<span>
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Answer:
The integers are 4 and 7 or -2 and 1.
Step-by-step explanation:
You can make a system of equations with the description of the two integers.
1. x = y + 3
2. 2x + 2 = y^2
The simplest and the fastest way to solve this system in this case is substitution. You can substitute x for y + 3 in the second equation.
1. x = y + 3
2. 2(y + 3) + 2 = y^2
Now simplify and solve the second one. For convenience, I will just disregard the first equation for now.
2y + 6 + 2 = y^2
y^2 - 2y - 8 = 0
You can factor this equation to solve for y.
(y - 4) (y + 2) = 0
y = 4, y = -2
Now we can substitute the value of y for x in the first equation.
x = 7, x = 1
Answer:
z = x^3 +1
Step-by-step explanation:
Noting the squared term, it makes sense to substitute for that term:
z = x^3 +1
gives ...
16z^2 -22z -3 = 0 . . . . the quadratic you want
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<em>Solutions derived from that substitution</em>
Factoring gives ...
16z^2 -24z +2z -3 = 0
8z(2z -3) +1(2z -3) = 0
(8z +1)(2z -3) = 0
z = -1/8 or 3/2
Then we can find x:
x^3 +1 = -1/8
x^3 = -9/8 . . . . . subtract 1
x = (-1/2)∛9 . . . . . one of the real solutions
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x^3 +1 = 3/2
x^3 = 1/2 = 4/8 . . . . . . subtract 1
x = (1/2)∛4 . . . . . . the other real solution
The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.
